%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL513+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:06:48 PM UTC 2026
% Result : Theorem 145.34s 28.29s
% Output : CNFRefutation 145.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 16
% Syntax : Number of formulae : 226 ( 111 unt; 0 def)
% Number of atoms : 366 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 268 ( 128 ~; 123 |; 2 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 404 ( 0 sgn 402 !; 2 ?; 346 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',equivalence_2) ).
fof(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(f18,axiom,
( kn3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f43,conjecture,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f44,negated_conjecture,
~ equivalence_2,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ equivalence_2,
inference(flattening,[],[f44]) ).
fof(f46,plain,
( kn3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f47,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f48,plain,
( kn1
=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f49,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
=> equivalence_2 ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f51,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f54,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f55,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f54]) ).
fof(f57,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| equivalence_2 ),
inference(ennf_transformation,[],[f49]) ).
fof(f58,plain,
( ~ kn1
| ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(ennf_transformation,[],[f48]) ).
fof(f59,plain,
( ~ kn2
| ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f60,plain,
( ~ kn3
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(ennf_transformation,[],[f46]) ).
fof(f61,plain,
( ~ op_or
| ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f62,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f63,plain,
( ~ op_equiv
| ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f64,plain,
( ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0)))
| equivalence_2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f57]) ).
fof(f65,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f67,plain,
( ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0)))
| equivalence_2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f68,plain,
! [X0] :
( ~ kn1
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(cnf_transformation,[],[f58]) ).
fof(f69,plain,
! [X0,X1] :
( ~ kn2
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ kn3
| is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(cnf_transformation,[],[f60]) ).
fof(f71,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f61]) ).
fof(f72,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f73,plain,
! [X0,X1] :
( ~ op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f77,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f78,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f79,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f80,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f82,plain,
op_or,
inference(cnf_transformation,[],[f40]) ).
fof(f83,plain,
op_implies_and,
inference(cnf_transformation,[],[f41]) ).
fof(f84,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f85,plain,
~ equivalence_2,
inference(cnf_transformation,[],[f45]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_51,plain,
( equivalence_2
| ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0))) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_52,plain,
! [X0: $i] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( not(and(not(X0),not(X1))) = or(X0,X1) )
| ~ op_or ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( not(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) )
| ~ op_equiv ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_61,plain,
modus_ponens,
inference(cnf_transformation,[],[f77]) ).
tcf(c_62,plain,
kn1,
inference(cnf_transformation,[],[f78]) ).
tcf(c_63,plain,
kn2,
inference(cnf_transformation,[],[f79]) ).
tcf(c_64,plain,
kn3,
inference(cnf_transformation,[],[f80]) ).
tcf(c_66,plain,
op_or,
inference(cnf_transformation,[],[f82]) ).
tcf(c_67,plain,
op_implies_and,
inference(cnf_transformation,[],[f83]) ).
tcf(c_68,plain,
op_equiv,
inference(cnf_transformation,[],[f84]) ).
tcf(c_69,negated_conjecture,
~ equivalence_2,
inference(cnf_transformation,[],[f85]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_53,c_63,c_53]) ).
tcf(c_80,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(X0,X0))),
inference(global_subsumption_just,[status(thm)],[c_52,c_62,c_52]) ).
tcf(c_83,plain,
~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0))),
inference(global_subsumption_just,[status(thm)],[c_51,c_69,c_51]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_56,c_67,c_56]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_61,c_49]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_91]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_55,c_66,c_55]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] : and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_57,c_68,c_57]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
inference(global_subsumption_just,[status(thm)],[c_54,c_64,c_54]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_93,c_88]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
inference(demodulation,[status(thm)],[c_99,c_152]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i,X2: $i] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_88,c_152]) ).
tcf(c_376,plain,
! [X0: $i] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_80,c_92]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_77,c_92]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(not(X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_152,c_92]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i] : and(or(X0,X1),implies(X1,not(X0))) = equiv(not(X0),X1),
inference(superposition,[status(thm)],[c_152,c_96]) ).
tcf(c_396,plain,
! [X0: $i] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[status(thm)],[c_96,c_80]) ).
tcf(c_416,plain,
! [X0: $i] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_152,c_80]) ).
tcf(c_440,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[c_96,c_377]) ).
tcf(c_446,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(not(X0),X1),or(and(X1,X2),implies(X2,X0)))),
inference(superposition,[status(thm)],[c_88,c_153]) ).
tcf(c_511,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(equiv(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_394,c_377]) ).
tcf(c_733,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(and(X1,X2),not(and(X2,X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_153,c_92]) ).
tcf(c_755,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))),
inference(light_normalisation,[status(thm)],[c_446,c_152]) ).
tcf(c_759,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),or(and(X1,not(X2)),or(X2,X0)))),
inference(superposition,[status(thm)],[c_152,c_755]) ).
tcf(c_760,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(and(X1,X2),implies(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_755,c_92]) ).
tcf(c_775,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))),
inference(demodulation,[status(thm)],[c_759,c_365]) ).
tcf(c_779,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_775,c_92]) ).
tcf(c_3694,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_779,c_92]) ).
tcf(c_3810,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(and(X1,X1),X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_80,c_3694]) ).
tcf(c_3811,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,and(X1,X2))) ),
inference(superposition,[status(thm)],[c_77,c_3694]) ).
tcf(c_3813,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(equiv(X1,X1),X0))
| ~ is_a_theorem(or(X0,implies(X1,X1))) ),
inference(superposition,[status(thm)],[c_396,c_3694]) ).
tcf(c_3828,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(not(X1),X1),X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_365,c_3810]) ).
tcf(c_3835,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X0,and(X2,X2)))
| ~ is_a_theorem(or(and(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_3810,c_3811]) ).
tcf(c_3843,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(or(X1,X1),X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(demodulation,[status(thm)],[c_3828,c_152]) ).
tcf(c_3851,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X1,X1))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_3843,c_92]) ).
tcf(c_3859,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X0,and(X2,X2)))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_365,c_3835]) ).
tcf(c_3905,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(equiv(X0,X0),and(X1,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_760,c_3813]) ).
tcf(c_3925,plain,
! [X0: $i] : is_a_theorem(or(X0,and(equiv(X0,X0),equiv(X0,X0)))),
inference(superposition,[status(thm)],[c_396,c_3859]) ).
tcf(c_3941,plain,
! [X0: $i] : is_a_theorem(or(equiv(X0,X0),X0)),
inference(superposition,[status(thm)],[c_3925,c_3811]) ).
tcf(c_3948,plain,
! [X0: $i] :
( is_a_theorem(equiv(not(X0),not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_3941,c_3851]) ).
tcf(c_4071,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,equiv(X0,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_3905,c_3811]) ).
tcf(c_4108,plain,
! [X0: $i] :
( is_a_theorem(or(X0,not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_3948,c_511]) ).
tcf(c_4119,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_4108,c_3851]) ).
tcf(c_4130,plain,
! [X0: $i] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(or(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_3810,c_4119]) ).
tcf(c_4216,plain,
! [X0: $i] :
( is_a_theorem(and(equiv(X0,X0),equiv(X0,X0)))
| ~ is_a_theorem(or(X0,and(equiv(X0,X0),equiv(X0,X0)))) ),
inference(superposition,[status(thm)],[c_4071,c_4130]) ).
tcf(c_4221,plain,
! [X0: $i] : is_a_theorem(and(equiv(X0,X0),equiv(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_4216,c_3925]) ).
tcf(c_4240,plain,
! [X0: $i] : is_a_theorem(equiv(X0,X0)),
inference(superposition,[status(thm)],[c_4221,c_377]) ).
tcf(c_4504,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_4240,c_440]) ).
tcf(c_4506,plain,
! [X0: $i] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[status(thm)],[c_4240,c_511]) ).
tcf(c_4511,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_4504,c_3694]) ).
tcf(c_4733,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_4506,c_4511]) ).
tcf(c_4741,plain,
! [X0: $i] : is_a_theorem(or(X0,equiv(X0,X0))),
inference(superposition,[status(thm)],[c_3941,c_4511]) ).
tcf(c_4915,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),and(X0,not(X1)))),
inference(superposition,[status(thm)],[c_88,c_4733]) ).
tcf(c_4919,plain,
! [X0: $i] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_4733,c_3851]) ).
tcf(c_5003,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_4915,c_3811]) ).
tcf(c_5552,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(not(X0),or(X0,X1))),
inference(superposition,[status(thm)],[c_152,c_5003]) ).
tcf(c_5678,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(not(X0))) ),
inference(superposition,[status(thm)],[c_5552,c_378]) ).
tcf(c_6753,plain,
! [X0: $i] :
( is_a_theorem(not(not(equiv(X0,X0))))
| ~ is_a_theorem(or(X0,equiv(X0,X0))) ),
inference(superposition,[status(thm)],[c_4071,c_4919]) ).
tcf(c_6757,plain,
! [X0: $i] : is_a_theorem(not(not(equiv(X0,X0)))),
inference(forward_subsumption_resolution,[status(thm)],[c_6753,c_4741]) ).
tcf(c_6764,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(equiv(X0,X0),X1)),
inference(superposition,[status(thm)],[c_6757,c_5678]) ).
tcf(c_6774,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,equiv(X1,X1))),
inference(superposition,[status(thm)],[c_6764,c_3811]) ).
tcf(c_6788,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,and(equiv(X1,X1),equiv(X1,X1)))),
inference(superposition,[status(thm)],[c_6774,c_3835]) ).
tcf(c_38391,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_4240,c_440]) ).
tcf(c_38392,plain,
! [X0: $i] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[status(thm)],[c_152,c_38391]) ).
tcf(c_38513,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,X0))
| ~ is_a_theorem(not(and(X0,X1))) ),
inference(superposition,[status(thm)],[c_760,c_378]) ).
tcf(c_38523,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_779,c_92]) ).
tcf(c_38683,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(and(X1,X1),X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_80,c_38523]) ).
tcf(c_38684,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,and(X1,X2))) ),
inference(superposition,[status(thm)],[c_77,c_38523]) ).
tcf(c_38690,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_38391,c_38523]) ).
tcf(c_38706,plain,
! [X0: $i] : is_a_theorem(or(and(not(X0),not(X0)),X0)),
inference(superposition,[status(thm)],[c_416,c_38690]) ).
tcf(c_38707,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_38392,c_38690]) ).
tcf(c_38708,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(not(and(X2,X0)),and(X1,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_733,c_38690]) ).
tcf(c_38718,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),and(X0,not(X1)))),
inference(superposition,[status(thm)],[c_88,c_38707]) ).
tcf(c_38726,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),X0)),
inference(demodulation,[status(thm)],[c_38706,c_152,c_365]) ).
tcf(c_38728,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,or(X1,X1))) ),
inference(superposition,[status(thm)],[c_38726,c_38523]) ).
tcf(c_38729,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_38726,c_92]) ).
tcf(c_38730,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(or(X0,X1),and(not(X0),not(X1)))),
inference(superposition,[status(thm)],[c_152,c_38718]) ).
tcf(c_38745,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(not(X1),X1),X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_365,c_38683]) ).
tcf(c_38753,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,not(and(X0,X1)))),
inference(superposition,[status(thm)],[c_38707,c_38684]) ).
tcf(c_38754,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_38718,c_38684]) ).
tcf(c_38755,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(not(X0),or(X0,X1))),
inference(superposition,[status(thm)],[c_38730,c_38684]) ).
tcf(c_38756,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(equiv(X0,X0),X1)),
inference(superposition,[status(thm)],[c_6788,c_38684]) ).
tcf(c_38761,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(or(X1,X1),X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(demodulation,[status(thm)],[c_38745,c_152]) ).
tcf(c_38768,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X1,X1))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_38761,c_92]) ).
tcf(c_38792,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),X0)),
inference(superposition,[status(thm)],[c_38754,c_38690]) ).
tcf(c_38797,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,equiv(X1,X1))),
inference(superposition,[status(thm)],[c_38756,c_38684]) ).
tcf(c_38799,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(or(X0,X1),not(X0))),
inference(superposition,[status(thm)],[c_152,c_38792]) ).
tcf(c_38804,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(X0,implies(and(X0,X1),X2))),
inference(superposition,[status(thm)],[c_38792,c_38684]) ).
tcf(c_38824,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[status(thm)],[c_38753,c_378]) ).
tcf(c_38836,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_38799,c_38768]) ).
tcf(c_38860,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,not(and(X2,X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_38708,c_38684]) ).
tcf(c_38902,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(implies(and(X0,X1),X2),X0)),
inference(superposition,[status(thm)],[c_38804,c_38690]) ).
tcf(c_38999,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(not(X1))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_38824,c_38513]) ).
tcf(c_39304,plain,
! [X0: $i] : is_a_theorem(or(X0,not(or(X0,X0)))),
inference(superposition,[status(thm)],[c_38707,c_38728]) ).
tcf(c_39311,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(X0,implies(and(or(X0,X0),X1),X2))),
inference(superposition,[status(thm)],[c_38902,c_38728]) ).
tcf(c_39321,plain,
! [X0: $i] : is_a_theorem(or(not(or(X0,X0)),X0)),
inference(superposition,[status(thm)],[c_39304,c_38690]) ).
tcf(c_39380,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X2,not(X0)))
| ~ is_a_theorem(not(or(X0,X1))) ),
inference(superposition,[status(thm)],[c_38755,c_38999]) ).
tcf(c_39456,plain,
! [X0: $i] :
( is_a_theorem(not(or(not(X0),not(X0))))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_39321,c_38768]) ).
tcf(c_41450,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,implies(X2,X0)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_88,c_38860]) ).
tcf(c_41502,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,implies(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_41450,c_152]) ).
tcf(c_41508,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_152,c_41502]) ).
tcf(c_41518,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(implies(X1,X0),X2))
| ~ is_a_theorem(or(X0,implies(X1,X0))) ),
inference(superposition,[status(thm)],[c_41502,c_38836]) ).
tcf(c_41536,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(or(X1,X0),X2))
| ~ is_a_theorem(or(X0,or(X1,X0))) ),
inference(superposition,[status(thm)],[c_41508,c_38836]) ).
tcf(c_41538,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,or(X1,X0))) ),
inference(superposition,[status(thm)],[c_41508,c_38729]) ).
tcf(c_42781,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,not(not(X0))))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_39456,c_39380]) ).
tcf(c_42808,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,not(not(equiv(X1,X1))))),
inference(superposition,[status(thm)],[c_38797,c_42781]) ).
tcf(c_42861,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,not(not(equiv(X1,X1))))),
inference(superposition,[status(thm)],[c_152,c_42808]) ).
tcf(c_42909,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(not(not(equiv(X0,X0))),X1)),
inference(superposition,[status(thm)],[c_42861,c_38836]) ).
tcf(c_43560,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(implies(and(or(X0,X0),X1),X0),X2)),
inference(superposition,[status(thm)],[c_39311,c_41518]) ).
tcf(c_43645,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(or(X0,not(not(equiv(X1,X1)))),X2)),
inference(superposition,[status(thm)],[c_42909,c_41536]) ).
tcf(c_83808,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(X0,implies(and(or(X1,X1),X2),X1))),
inference(superposition,[status(thm)],[c_43560,c_41538]) ).
tcf(c_85411,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(X0,or(X1,not(not(equiv(X2,X2)))))),
inference(superposition,[status(thm)],[c_43645,c_41538]) ).
tcf(c_189603,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(not(not(equiv(X0,X0))))
| ~ is_a_theorem(or(not(equiv(X0,X0)),X1)) ),
inference(instantiation,[status(thm)],[c_378]) ).
tcf(c_192964,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(and(or(X1,X1),X2),X1))
| ~ is_a_theorem(not(not(equiv(X0,X0))))
| ~ is_a_theorem(or(not(equiv(X0,X0)),implies(and(or(X1,X1),X2),X1))) ),
inference(instantiation,[status(thm)],[c_189603]) ).
tcf(c_192965,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(not(equiv(X0,X0)),implies(and(or(X1,X1),X2),X1))),
inference(instantiation,[status(thm)],[c_83808]) ).
tcf(c_292035,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_4240,c_440]) ).
tcf(c_292036,plain,
! [X0: $i] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[status(thm)],[c_152,c_292035]) ).
tcf(c_292084,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(and(or(X1,X1),X2),X1))
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[status(thm)],[c_83808,c_378]) ).
tcf(c_292137,plain,
! [X1: $i,X2: $i] : is_a_theorem(implies(and(or(X1,X1),X2),X1)),
inference(global_subsumption_just,[status(thm)],[c_292084,c_6757,c_192964,c_192965]) ).
tcf(c_292138,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(or(X0,X0),X1),X0)),
inference(renaming,[status(thm)],[c_292137]) ).
tcf(c_292139,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(or(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_292138,c_92]) ).
tcf(c_292190,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_376,c_292139]) ).
tcf(c_292197,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,not(not(equiv(X1,X1))))),
inference(superposition,[status(thm)],[c_85411,c_292190]) ).
tcf(c_292496,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_779,c_92]) ).
tcf(c_292552,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,and(X1,X2))) ),
inference(superposition,[status(thm)],[c_77,c_292496]) ).
tcf(c_292556,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_292035,c_292496]) ).
tcf(c_292604,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,X0))
| ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_152,c_292496]) ).
tcf(c_292624,plain,
! [X0: $i] : is_a_theorem(or(and(not(X0),not(X0)),X0)),
inference(superposition,[status(thm)],[c_416,c_292556]) ).
tcf(c_292625,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_292036,c_292556]) ).
tcf(c_292663,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),and(X0,not(X1)))),
inference(superposition,[status(thm)],[c_88,c_292625]) ).
tcf(c_292679,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),X0)),
inference(demodulation,[status(thm)],[c_292624,c_152,c_365]) ).
tcf(c_292681,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,or(X1,X1))) ),
inference(superposition,[status(thm)],[c_292679,c_292496]) ).
tcf(c_292707,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,not(and(X0,X1)))),
inference(superposition,[status(thm)],[c_292625,c_292552]) ).
tcf(c_292708,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_292663,c_292552]) ).
tcf(c_292739,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),X0)),
inference(superposition,[status(thm)],[c_292708,c_292556]) ).
tcf(c_292741,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(or(X0,X1),not(X0))),
inference(superposition,[status(thm)],[c_152,c_292739]) ).
tcf(c_293334,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(or(X0,X0),X1))),
inference(superposition,[status(thm)],[c_292739,c_292681]) ).
tcf(c_293410,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(or(X0,X0),X1),X0)),
inference(superposition,[status(thm)],[c_293334,c_292556]) ).
tcf(c_293421,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(or(or(X0,X0),or(X0,X0)),X1))),
inference(superposition,[status(thm)],[c_293410,c_292681]) ).
tcf(c_294056,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,X0))
| ~ is_a_theorem(or(and(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_292707,c_292604]) ).
tcf(c_294063,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,or(X0,X2)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_292741,c_292604]) ).
tcf(c_294093,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(not(equiv(X0,X0)),X1)) ),
inference(superposition,[status(thm)],[c_292197,c_292604]) ).
tcf(c_294335,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(not(and(X2,X0)),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_733,c_294056]) ).
tcf(c_294336,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(implies(X2,X0),X1))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_760,c_294056]) ).
tcf(c_294409,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(or(X0,X2),X1))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_294063,c_292556]) ).
tcf(c_294816,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,implies(X1,X0))) ),
inference(superposition,[status(thm)],[c_294336,c_292190]) ).
tcf(c_297209,plain,
! [X0: $i] : is_a_theorem(implies(or(or(X0,X0),or(X0,X0)),X0)),
inference(superposition,[status(thm)],[c_293421,c_294816]) ).
tcf(c_297216,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(or(X0,X0),or(X0,X0))) ),
inference(superposition,[status(thm)],[c_297209,c_92]) ).
tcf(c_297240,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,or(X0,X0))) ),
inference(superposition,[status(thm)],[c_294409,c_297216]) ).
tcf(c_299738,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(not(equiv(X1,X0)),X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_96,c_294335]) ).
tcf(c_300064,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_299738,c_294093]) ).
tcf(c_300134,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(or(and(X0,X1),not(and(X1,X0))),X2)),
inference(superposition,[status(thm)],[c_153,c_300064]) ).
tcf(c_300324,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(X0,X1),not(and(X1,X0)))),
inference(superposition,[status(thm)],[c_300134,c_297240]) ).
tcf(c_300511,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(not(and(X0,X1)),X1)),
inference(superposition,[status(thm)],[c_300324,c_294056]) ).
tcf(c_300521,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,not(and(X1,X0)))),
inference(superposition,[status(thm)],[c_300511,c_292556]) ).
tcf(c_300547,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,X1))
| ~ is_a_theorem(or(and(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_300521,c_292604]) ).
tcf(c_302662,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(implies(and(X0,X1),X2),X1)),
inference(superposition,[status(thm)],[c_292708,c_300547]) ).
tcf(c_302782,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(X0,implies(and(X1,X0),X2))),
inference(superposition,[status(thm)],[c_302662,c_292556]) ).
tcf(c_302796,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(implies(X0,X1),implies(equiv(X1,X0),X2))),
inference(superposition,[status(thm)],[c_96,c_302782]) ).
tcf(c_302833,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(superposition,[status(thm)],[c_302796,c_294816]) ).
tcf(c_302834,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_83,c_302833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL513+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.42 % Computer : n006.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Wed Sep 23 23:36:26 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.48 Running first-order theorem proving
% 0.16/0.48 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.49
% 0.23/0.49 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.49
% 0.23/0.49 % Detected problem language: tptp
% 0.23/0.51 % Proving...
% 145.34/28.29 % SZS status Started for theBenchmark.p
% 145.34/28.29 % SZS status Theorem for theBenchmark.p
% 145.34/28.29
% 145.34/28.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 145.34/28.29
% 145.34/28.29 % ------ iProver source info
% 145.34/28.29
% 145.34/28.29 % git: date: 2026-07-19 20:42:38 +0200
% 145.34/28.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 145.34/28.29 % git: non_committed_changes: false
% 145.34/28.29
% 145.34/28.29 % ------ Parsing...
% 145.34/28.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 145.34/28.29
% 145.34/28.29 % ------ Preprocessing... sup_sim: 2 sf_s rm: 10 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 145.34/28.29
% 145.34/28.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 145.34/28.29
% 145.34/28.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 145.34/28.29 % ------ Proving...
% 145.34/28.29 % ------ Problem Properties
% 145.34/28.29
% 145.34/28.29 %
% 145.34/28.29 % clauses 9
% 145.34/28.29 % conjectures 0
% 145.34/28.29 % EPR 0
% 145.34/28.29 % Horn 9
% 145.34/28.29 % unary 7
% 145.34/28.29 % binary 1
% 145.34/28.29 % lits 12
% 145.34/28.29 % lits eq 4
% 145.34/28.29 % fd_pure 0
% 145.34/28.29 % fd_pseudo 0
% 145.34/28.29 % fd_cond 0
% 145.34/28.29 % fd_pseudo_cond 1
% 145.34/28.29 % AC symbols 0
% 145.34/28.29
% 145.34/28.29 % ------ Input Options Time Limit: Unbounded
% 145.34/28.29
% 145.34/28.29
% 145.34/28.29 % ------
% 145.34/28.29 % Current options:
% 145.34/28.29 % ------
% 145.34/28.29
% 145.34/28.29
% 145.34/28.29 %
% 145.34/28.29
% 145.34/28.29 % ------ Proving...
% 145.34/28.29 %
% 145.34/28.29
% 145.34/28.29 % SZS status Theorem for theBenchmark.p
% 145.34/28.29
% 145.34/28.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 145.34/28.29
% 145.34/28.29
%------------------------------------------------------------------------------